Journal Article

A Unified Neural Background‐Error Covariance Model for Midlatitude and Tropical Atmospheric Data Assimilation

Zaplotnik, Žiga, Melinc, Boštjan, Perkan, Uroš

2026

Overview

Estimating and modeling background‐error covariances remains a core challenge in variational data assimilation (DA). Operational systems typically approximate these covariances by transformations that separate geostrophically balanced components from unbalanced inertia‐gravity modes—an approach well‐suited for the midlatitudes but less applicable in the tropics, where different physical balances prevail. This study estimates background‐error covariances in a reduced‐dimension latent space learned by a neural‐network autoencoder (AE). The AE was trained using 40 years of ERA5 reanalysis data, enabling it to capture flow‐dependent atmospheric balances from a diverse set of weather states. We demonstrate that performing DA in the latent space yields analysis increments that preserve multivariate horizontal and vertical physical balances in both tropical and midlatitude atmosphere. Assimilating a single 500 hPa geopotential height observation in the midlatitudes produces increments consistent with geostrophic and thermal wind balance, while assimilating a total column water vapor observation with a positive departure in the nearly‐saturated tropical atmosphere generates an increment resembling the tropical response to (latent) heat‐induced perturbations. The resulting increments are localized and flow‐dependent, and shaped by orography and land‐sea contrasts. Forecasts initialized from these analyses exhibit realistic weather evolution, including the excitation of an eastward‐propagating Kelvin wave in the tropics. Finally, we explore the transition from using synthetic ensembles and a climatology‐based background error covariance matrix to an operational ensemble of data assimilations. Despite significant compression‐induced variance loss in some variables, latent‐space assimilation produces balanced, flow‐dependent increments—highlighting its potential for ensemble‐based latent‐space 4D‐Var. Plain Language Summary Accurately estimating the current state of the atmosphere is essential for reliable weather forecasting. This estimate, called the initial condition, is produced through data assimilation (DA)—a process that combines previous short forecast with new observations. An important part of this process involves describing how forecast errors relate across space and between atmospheric variables. This relationship determines how the influence of each new observation is spread in a physically consistent way. Traditional weather models rely on statistical or theoretical assumptions to describe these error relationships. While effective in the midlatitudes, these assumptions often fail in the tropics, where different physical processes dominate. In this study, we explore a new approach that learns a simplified low‐dimensional representation of the atmosphere using a neural network trained on 40 years of reconstructed weather data. We show that performing DA of new observations in this learned “latent space” produces realistic updates that respect known atmospheric balances both in the tropics and midlatitudes and adapt to the current weather situation. It also works with forecast ensembles used in operational weather centers. These results suggest that DA in latent space could offer a more flexible and efficient way to improve weather forecasts. Key Points The background‐error covariances in a machine learning‐based variational data assimilation framework are studied The method captures both tropical and midlatitude atmospheric balances in the background‐error covariance model The approach works with both climatological and ensemble‐based background‐error covariance matrices

• Publisher: John Wiley & Sons, Inc,American Geophysical Union (AGU)
• Subject: Atmosphere / atmospheric balances / Atmospheric data / background‐error covariances / Climatology / Compression / Data assimilation / Data collection / Dynamic height / Experiments / Geopotential height / Inertia / Kelvin waves / latent space / Latitude / neural network data assimilation / Neural networks / Orography / Thermal winds / Tropical atmosphere / tropical data assimilation / Tropical environments / Variables / variational data assimilation / Water vapor / Water vapour